Spatial strength centrality and the effect of spatial embeddings on network architecture

Area of Science:

• Network Science
• Statistical Physics
• Computational Social Science

Background:

• Network models often assume nodes exist in a latent space influencing connections.
• Existing synthetic network models lack explicit spatial embedding considerations.

Purpose of the Study:

• To extend synthetic network models into spatial network models.
• To investigate the impact of spatial embeddings on network structure and properties.
• To introduce and analyze a new metric, spatial strength centrality.

Main Methods:

• Embedding network nodes in Euclidean space.
• Modifying existing models (geographical fitness, preferential attachment, configuration) for spatial properties.
• Employing Gaussian-distributed fitnesses in the geographical fitness model.
• Defining and calculating spatial strength centrality.

Main Results:

• Successfully developed spatial versions of geographical fitness, preferential attachment, and configuration models.
• Demonstrated that longer edges occur with lower probabilities in spatial networks.
• Examined spatial strength centrality across diverse real-world and synthetic networks.

Conclusions:

• Spatial embeddings significantly influence network structure.
• The developed spatial network models provide a more realistic representation of many real-world systems.
• Spatial strength centrality is a valuable metric for quantifying the impact of spatial embedding on network topology.